Finite Group DatabasebetaFinite Group Databasebeta| order | 8518 |
| automorphism | Aut(G) order 18134822 |
| homology | Abelianization (H1) = C2 · Schur multiplier (H2) = C1 |
| dihedral | D4259 |
| unambiguous semidirect product | C4259⋊C2 |
| Fitting, socle, derived, Sylow | C4259 ⋊ C2 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C4259 | C2 |
| LCS | G ▷ C4259 | |
| UCS | C1 | |
4 conjugacy classes of subgroups.
Polycyclic presentation:
2,4259|b^a=b^42582131 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C2×D4259, C3×D4259, D12777 |
| maximal normal subgroup of | C2×D4259, C3×D4259 |
| maximal quotient of | Dic4259, C2×D4259, C3×D4259, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8518, 1);